The Rapture of Nerds by Charles Stross and Cory Doctorow.
Here's the scene:
“Yes, O Mistress?”
“What’s going on?”
“639,219 called for a shardwide resource audit. The capabilities
platform determined that you were consuming a disproportionate amount
of computation to run substantively duplicative processes. So as you
hadn’t paid for them all the extraneous threads were suspended; the
least duplicative were niced down to minimal sentience.”
“That’s not fair!”
"Well,” the djinni says, “you’re the one who cranked herself up to eleven. Where did you think the cycles for that particular enhancement would come from? The second law of thermodynamics hasn’t been repealed, you know: energy costs. For every moment you spend contemplating your awesome might with preternatural awareness, you’re consuming a concomitant lump of compute-time and producing waste-heat that needs to be convected into space without being transformed into thrust or spin, which is no simple process and requires its own secondary computation, which generates more waste-heat and consumes more resources.”
You're right that the main character is a latecomer to the high tech world - as the wiki page says:
The book, set in the late 21st century, takes a generally comic look
at the technological singularity through the eyes of Huw, a
technophobic member of a "Tech Jury Service" tasked with determining
the value of various technological innovations and deciding whether to
The bill might have been presented by a robot police officer.
There's no robot police officer, but there's a cyborg judge (Judge Rosa Giuliani) who is basically Judge Judy in a Dalek body.